Macromolecules 1985,18, 2784-2786
2784
Acknowledgment. This work was supported by Nippon Zeon Co. and the National Science Foundation (Grant DMR 83-10522). Registry No. (BIS).(MAPTAC).(acrylamide) (copolymer), 98587-56-5; (BIS).(SSS) (copolymer), 91293-65-1; acetone, 67-64-1; water, 7732-18-5.
References and Notes (1) T. Tanaka, Phys. Rev. Lett., 40, 820 (1978). (2) T. Tanaka, D. J. Fillmore, S.-T.Sun, I. Nishio, G. Swislow, and A. Shah, Phys. Reu. Lett., 45, 1636 (1980). (3) M. Ilavsky, Macromolecules, 15, 782 (1982). (4) J. Hrouz, M. Ilavsky, K. Ulbrich, and J. Kopecek, Eur. Polym. J., 17, 361 (1981). (5) M. Ilavsky, J. Hrouz, and K. Ulbrich, Polym. Bull. (Berlin),7, 107 (1982). (6) M. Ilavsky, Polymer, 22, 1687 (1981). (7) T. Tanaka, Sci. Am., 244, 110 (1981). (8) I. Ohmine and T. Tanaka, J . Chem. Phys., 11, 5725 (1982). (9) J. Ricka and T. Tanaka, Macromolecules, 18, 83 (1985). (10) Y. Hirokawa and T. Tanaka, in ”Microbial Adhesion and
Aggregation”, K. C. Marshall, Ed., Springer-Verlag, Heidelberg and New York, 1984; see also, D. Nicoli, C. Young, T. Tanaka, A. Pollak, and G. Whitesides, Macromolecules, 16,887 (1983). (11) T. Tanaka, I. Nishio, S.-T.Sun, and S. Ueno-Nishio, Science (Washington,D.C.), 218, 467 (1982). (12) S. Katayama, Y. Hirokawa, and T. Tanaka, Macromolecules,
nated polyethylene (CPE) are immiscible even when the CPE has the same C1 content as PVC.2 In this context, CPE may be considered as a random copolymer of CH2 (zA) and CHCl (=B), while PVC is the alternating copolymer composed of these units. The theoretical formulations presented below will be compared to recent experimental observations of the phase behavior of blends of CPEa2 It will be shown that these data allow the determination of the various interaction parameters required by theory. The Model. The free energy of mixing for a mixture of two copolymers that differ only in polymer composition is given by3 A G / R T = (@AB/IV) In @AB + (@AB’/”I In @AB’ + @AB@AB’(fA
where 4 A B is the volume fraction of one copolymer with degree of polymerization N and composition fA, while @AB’ is the volume fraction of the other copolymer with degree of polymerization ”and composition g A ( @ m + @AB’ = 1). This free energy is identical with the usual Flory-Huggins one, when the following identification is made: Xblend
17, 2641 (1984). (13) Permanent address: Development and Research Center, Nippon Zeon Co., Kawasaki, 210 Japan. (14) Department of Applied Biological Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139.
Yoshitsugu Hirokawa,13Toyoichi Tanaka, and Eriko Sato*14 Department of Physics and Center for Materials Science and Engineering, Massachusetts Institute of Technology Cambridge, Massachusetts 02139 Received June 26, 1985
Copolymer/Copolymer Blends: Effect of Sequence Distribution on Miscibility In a previous paper,l we have discussed the effect of the sequence distribution of monomer units in a copolymer on the phase behavior of copolymerfhomopolymer blends. Our model yielded an improvement to Flory-Huggins type theories for mixturs involving copolymers in that it was possible to make a distinction between the copolymer types (random, block, etc.) participating in the mixture. This was accomplished by introducing a parameter, 9, which described the binary sequence distribution of the monomers in the copolymer. By varying 8 , we could describe a block, random, or alternating copolymer. Further, we assumed that the interaction energy between a monomer of homopolymer C and the monomer A (or B) in the copolymer AB is mediated by the nearest neighbors chemically bonded to the A (or B) structural unit. W e showed that for a fixed composition, there is an optimal range of 9 values (or sequence distributions) for which the ABfC system may be miscible. In this communication, we apply the above model to the mixture of two copolymers that differ only in composition, one containing fA units of A comonomer and f B units of B comonomer + fB = 1)and the other g A units of A and g B units of B (gA + g B = 1). A special case of interest is where both copolymers have the same composition (fA = g A ) and differ only in the sequence distribution of their monomers. An interesting question is: Are there circumstances under which these polymers are immiscible? Experimentally it is known that blends of PVC and chlori-
vA
0024-9297/85/2218-2784$01.50/0
- gA)’XAB
(fA
(2)
- gA)*XAB
Here, we will consider a binary mixture of two copolymers with compositions fA and g A but assume that the interaction energy for an A-B pair is influenced by the units that are chemically bound to A (and B). This requires that all the possible pairs of triplets, with A or B occupying the central site, be enumerated. Next, the probability of occurrence for each specific triplet is calculated and an energy is assigned to each A-B interaction. To reduce the large number of x parameters required to properly describe the energetics, the following simplifications are introduced: it will be assumed that all A-A and B-B interactions are equivalent and equal to zero. Although there are 16 possible A-B interactions, a unique energy is assigned only to the triplet pairs (AAA-BBB) and (BAB-ABA): xAAA;.BB for the former and xBAB;.A for the latter. The remaining 14 pairs of A-B interacting triplets are assigned an average value of jiAB. The required pair probabilities fm, fBB and fAAare the joint probabilities of AB, BB, and AA pairs; @A and @B are the volume fractions of A and B comonomers for the copolymer with composition fA. These variables are related as follows: fA
= fAA + f A B ; fA
+fB
fB
= 1;
fA@AB
=
=
+ fBA;
fBB @A
fAB
+ @B = @AB
@A;
fB@AB
=
= fBA
(3)
@B
An identical set of relationships apply to the g.4 and g B variables with @A’ + @B’ = @AB’. triplet of the fA copolymer The probability of the interacting with the BBB triplet of the g A copolymer is given by the probability of the AAA configuration, @AfA)’, times the probability of the BBB configuration, @B’(gBB/gB)2, which yields @AB4AB’(fAAgBBI2/fAgB
(4)
Similarly, the probability of a BAB triplet interacting with an ABA triplet is 4AB4AB‘(fA&ABl2
/fAgB
(5)
On the other hand, an AAA-BBB triplet interaction involving the same fA copolymer is given by ( 1 - @AB’)@AB(fAAfBB)*/fAfB
and a BAB-ABA triplet interaction is given by 0 1985 American Chemical Society
(6)
Communications to the Editor 2785
Macromolecules, Vol. 18, No. 12, 1985 (7)
(1- 4AB’)d’ABfAB4/fAfB
Of course, relations identical with (6) and (7) apply for triplet interactions involving the gA copolymer (replace f by g). As previously stated,’ it is important to note that the term linear in the volume fraction variable $AB is not important in determining phase stability or equilibria and is ignored. Hence the terms in Xblend arising from the copolymer self-interactions, relations 6 and 7, enter with a minus sign. Collecting all terms, the total expression for the energy of interaction can be written as $AB$AB’Xblend, where
Xdist
=
Xblend
=
Xcomp
Xdist
(8)
Xcomp
=
XAB(fA - gA)’
(9)
+
[ ($ %)( [ (5 y)( -
- %)]Axb
+ (10)
where Axa E ZAB- XBAB~ABA
(11)
Axb E
(12)
and XAAA;BBB - jim
The “a” and “b” superscripts on Ax refer to “alternating” and “block” sequences, respectively. Since it is expected that XAMBBB > ZAB > XBAB;ABA or XAAA;BBB < XAB < X ~ A B ; Axa . A ,and Axb should almost always have the same sign. As in the previous calculation,’ we introduce the parameters 8 and 6 defined by f A B = 2efAfB (13) -1 5 6 5 1 (14) fA = f/2(1 6); fB = y2(1 - 6);
+
A block copolymer corresponds to 8 = 0, a random copolymer is described by 8 = ’/’, and 8 = 1 describes a purely alternating copolymer. The maximum value of 0 is given by’ emax
= (1 + 16II-l
(15)
Using eq 3, 13, and 14, one can express as functions of 0 and 6 all pair probabilities such as fAA,fBB, etc. Results and Discussion. A special case of the above equations is a blend of a 50:50 alternating copolymer (6 = 0 and 8 = 1)with a 5050 random copolymer (6’ = 0 and 0’ = ‘ / J . For this system xcomp = 0, but Xdist
Xdist
=
&!&A2
- fBfA2)&!&B2
- fAfB2)Axa + (fA3
- !$)]Axa
-
that the blend is miscible. Here, xUA;BBB > jiAB and the presence of the alternating copolymer dilutes the energetically unfavorable “blocky” interactions. In the second case, we set Axb = 0 and let Axa be positive, which yields an immiscible mixture. Here, jiAB > xBAB;+BA and the presence of the random copolymer acts to dilute the favorable interactions among alternating triplets. As previously r e p ~ r t e d , ~we- ~again see how the presence of a second component can mediate between unfavorable or favorable interactions. Another special case of interest is a mixture of two random copolymers (0 = 8’ = 1/2) that only differ in composition (6 # 6’). In this case, fU = fA2,fBB = fB2,fAB = fdB, etc. and eq 10 becomes
= (9Axa - Axb)/64
(16)
There are no AAA-BBB interactions possible between the alternating and random copolymers; they are only possible when a random copolymer interacts with another random copolymer. On the other hand, BAB-ABA interactions are possible among all of the copolymers. This preference for interactions involving alternating over blocky ones is reflected in eq 16; the coefficient of the Axa term is 9 times larger than that of the Axb term. It is also obvious that x h t (and thus Xblend) may be positive, which suggests that it is possible for alternating and random copolymers with the same composition (fA = gA) to be immiscible. Two specific cases of eq 16 yield further insight into the physics described by this equation. In the first case, Axa = 0, Axb is positive, and Xblend is negative, which implies
- gA3)&!B3 - fB3)AXb (17)
-
Notice that Xdist is invariant under the interchange f g, as it should be. The values of Axa and Axb can be obtained directly by applying our model to recent experimental observations. For mixtures of two polymers of CPE with different compositions, experiments2 have yielded the critical compositions a t 150 “cfor which Xblend = xcrit. Knowing these critical values of fA, fB, gA, and gB, we can calculate the critical values of f, fa, fBB, g, g, and gBB. (We have ignored the small fraction of CC1, moieties in the mixture, which is an order of magnitude smaller than the CHCl content.) Consequently, the only remaining unknowns are XFxAAA;BBB, and x B A B ; . A . These are easily obtained from a linear least-squares fit of the “apparent”, observed values of xCH2;CHC1 through the following equations: Xbiend(expt1) = ( f ~- gA)’xcH,,cHcl(apparent) (Ma) = ( f A - gA)’XCH,;CHCl + Xdist
(18b)
xCH,;CHCl(apparent) = XCH,;CHCI + Xdist/(fA - gA)2 (18c) In the initial regression of the data, zAB (A CH2, B = CHCl) was found not to be significantly different from zero; therefore, a subsequent regression was performed with ZAB set identically equal to zero. This yielded the following values for the remaining variables: xUA;.BB = 0.37 f 0.03 and x B ~ . A= -4.34 f 0.40. The large negative value of x B ~ ; A B A implies that an alternating pattern of CH2,CHCl is energetically more favorable than a random distribution of these substituents. Considering the hydrogen bonds that are encountered in PVC, this result seems intuitively correct. With these numbers for the x’s, Table I shows the predicted values for XCH,;CHCI, which can be compared to the experimental data in the adjacent column. The overall agreement between the predicted and observed values is within f0.05. We now have an insight into the fact that the “apparent” xcHsCHc1 varies with the degree of chlorination.’ More than one x parameter is required to describe the CH,-CHCl interaction. It can be seen from eq 8-12 and the calculation just performed that while the values of these x’s remain constant, it is the factors mulitplying the x’s that change as the copolymer compositions in the mixutre are altered. Specifically, the factors multiplying Axa and Axb VAB, fBB, fAA, ek.1 vary with varying f A , fB, gA, and gB. The variation in these factors contributes to the variation of the observed x with the degree of chlorination even though XAB,XAAA;BBB, and XBAB;ABA are constants. Having obtained these x values, we can substitute the numbers into eq 16 to arrive at Xblend for PVC and CPE of equivalent composition (fA = gA = 0.5). We calculate that Xblend is 0.60, which indicates that the mixture is im-
Macromolecules, Vol. 18, No. 12, 1985
2786 Communications to the Editor
Table I Values of
~ c H , ; c H c lat Various Values f Aand g A and 150 O C
fA
gA
0.690 0.678 0.665 0.652 0.639 0.625 0.595 0.564 0.530 0.493 0.453 0.410 0.363 0.338 0.312 0.285 0.257 0.227
0.766 0.759 0.754 0.749 0.743 0.737
0.727 0.721 0.715 0.711 0.707 0.703 0.685 0.644 0.473 0.416 0.384 0.360
experimentally obsd 0.42 0.36 0.30 0.25 0.22 0.19 0.14 0.10 0.069 0.050 0.037 0.028 0.023 0.025 0.091 0.14 0.15 0.14
of
theoreticallp calcd 0.32 0.30 0.27 0.25 0.23 0.20 0.16 0.12 0.085 0.056 0.033 0.020 0.0089 -0.0018 0.053 0.13 0.20 0.27
"These quantities are calculated by using eq 18c. The overall agreement between the calculated and observed values is within k0.05.
make the polymers incompatible. Comparing our formulas to recent experimental data has allowed us to obtain values for the relevant x parameters. Using these two x parameters, we have been able to obtain a good correlation between our predictions and experimental observations that vary over an order of magnitude in value. This gives us confidence that these x values may be further used to predict other trends. Acknowledgment. This work was supported by DARPA, Contract F49620-84-(2-0051. F.E.K. acknowledges also AFOSR support under Grant AFOSR 84-0033. Registry No. PVC (homopolymer), 9002-86-2.
References a n d Notes (1) Balazs, A. C.; Sanchez, I. C.; Epstein, I. R.; Karasz, F. E.;
MacKnight, W. J. Macromolecules, in press. (2) Ueda, H.; Karasz, F. E., to be published. (3) ten Brinke, G.; Karasz, F. E.; MacKnight, W. J. Macromolecules 1983,16, 1827. (4) Kambour, R. P.; Bendler, J. T.; Bopp, R. C. Macromolecules 1983, 16, 753. (5) Paul, D. R.; Barlow, J. W. Polymer 1984, 25, 487. (6) Polymers Division, National Bureau of Standards, Gaithersburg, MD 20899.
miscible, as experimentally observed., S u m m a r y . Applying our previous model of the effect of sequence distribution in AB/C systems to AB/AB blends, we have shown that even in mixtures where the copolymers differ only in chain microstructure, the effect of sequence distribution may be sufficiently large as to
Anna C. Balazs,* Frank E. Karasz, William J. MacKnight, Hiroyoshi Ueda, and Isaac C. Sanchez6 Polymer Science and Engineering Department University of Massachusetts Amherst, Massachusetts 01003 Received September 10, 1985
CORRECTIONS Matthew T.Bishop, Frank E.&ram,* Paul S . RUSSO, and Kenneth H.Langley: Solubility and Properties of a Poly(ary1 ether ketone) in Strong Acids. Volume 18, Number 1, January 1985, p 86. We wish to amend results reported in ref 1 for the interpretation of Zimm plots (Figure 3). The correct relations for molecular weights (M,) and second virial coefficients (A,) of the sulfonated and unsulfonated (subscripts s and u, respectively) polymers relative to the apparent (subscript a) results are (A?,), = b(fiw)a,(A?,), = and (A& = P2(A2),, where 6 = c,/c,. The corrected values should be used in place of those given in lines 3,4, and 6 in Table 1. The revised estimate of the persistence length of protonated, sulfonated PEEK is -32 A and that of expansion relative to freely rotating unmodified PEEK is 1.6-1.9. This expansion of PEEK in concentrated H2S04,which we still attribute primarily to relatively short-range steric and electrostatic interactions, is seen to be even less than previously estimated and further strengthens our essential conclusions. We are grateful to Dr. E. Nield for sending us a preprint of ref 2, which drew our attention to the error. (1)Bishop, M. T.; Karasz, F. E.; Russo, P. S.; Langley, K. H. Macromolecules 1985, 18, 86. (2) Devaux, J.; Delimoy, D.; Daoust, D.; Legras, R.; Mercier, J. P.; Strazielle, C . ; Nield, E. Polymer, in press.
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